Scanning Tunneling Microscopes (STMs) use the concept of vacuum tunneling to image topographic features of metal and semiconductor surfaces to atomic scale resolution. This is accomplished by scanning an atomically sharp tip close to the surface of the sample to be studied. A tip-to-sample voltage is introduced causing a tunneling current to flow across the gap between the scanning tip and surface under study when the gap is sufficiently small. The tunneling current varies exponentially in relation to changes in the gap width. In most STMs the tip is scanned parallel to the surface (in the X-Y plane) by means of X and Y piezoelectric transducers and the tip-to-sample distance or gap is controlled by a third Z axis piezoelectric transducer. A feedback system senses the tunneling current and maintains this current constant by electrically actuating the Z axis piezoelectric transducer. The use of the feedback system allows the tip to follow the surface profile of the sample. The feedback voltage used to actuate the Z axis piezoelectric transducer varies in relation to the scanned profile. By systematically scanning adjacent lines in the X-Y plane (as in television scanning) and outputting the feedback voltage, an electronic image of the surface can be obtained. The first STMs displayed images either as traces on an oscilloscope screen or as tracings on electronic chart recorders. Increasing sophistication of STMs has brought digitization and computerization to image capture, storage, and display.
Piezoelectric materials change their mechanical shape when placed in an electric field. As such, these materials are useful when fashioned into devices for high precision motor control; the X, Y, & Z axis transducers identified above are examples. However, these materials exhibit time dependent behavior in response to a change to an applied electric field. One component of this behavior is known in the art as "creep" in which the dimensions of the transducer continue to change for some time after a change in the applied field. A second component of this behavior is the non-linear response of the piezoelectric transducers to an applied voltage. It is these two components that result in the distortion of STM images. The apparent scan position of the tip will lag the actual position by an amount that increases with the length of each scanned line. For scanning tunneling microscopy, this displacement lag has a significant impact on the quality of the image because the precise positioning of the tip is critically important in developing an image with accurate dimensions and quality resolution. The result is an apparent decrease in feature dimensions related to the location of the feature in the direction of the scan and length of the scan line.
To try to compensate for the distortions introduced in the image, some STMs are configured to discard parts of the data. This is sometimes accomplished by collecting image data in only one direction of the STM's lateral scan. The acquisition of image data ceases at the end of one scan line and the tip returned to the starting x coordinate position of the next scan line before beginning image acquisition of the next scan line. This prior art approach does not prevent distortion but masks the distortion because when all scan lines are scanned in the same direction each line is distorted in an identical fashion. Another disadvantage of this approach is that the scanner probe has to traverse the surface twice for every scan line recorded, drastically reducing the image acquisition rate. Other methods (Wilson and Chiang, "Image Processing Techniques for Obtaining Registration Information with STM" Journal of Vacuum Science Technology, vol. A6, pp. 398, 1988; Gehrtz, et al., "STM of Machined Surfaces", Journal of Vacuum Science Technology, vol. A6, pp 432, 1988) take advantage of the natural symmetry in some surfaces and involve modifying the image until the proper symmetry is obtained. However, the disadvantage of this prior art approach is that the accuracy of these methods can only be assured when scanning surfaces with regular repeating structures, which are 3 uncommon in long scan (&gt;100.times.100 nm) STM work.
A calibration method (Okayama, et al., "Observation of Microfabricated Patterns by STMs", Journal of Vacuum Science Technology, vol A6, pp. 440, 1988) has also been used. However, a drawback of this method is that it requires complex circuitry to adjust the image based on the scan speed and length of the scan. Circuitry has been added (Newcomb and Flynn, "Improving the Linearity of Piezo-Electric Ceramic Actuators", Electronics Letters, vol 18, pp. 442, 1982) to improve linearity, but this also adds complexity to the electronics and its success depends on choice of piezoelectric material. Therefore it is an objective of the present invention to provide a means for image correction without the penalties associated with the methods defined above.